LMFDB - Group of Dirichlet characters of modulus 6024

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6024)

pari: g = idealstar(,6024,2)

Character group

sage: G.order() pari: g.no
Order	=	2000
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{250}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6024}(4519,\cdot)$, $\chi_{6024}(3013,\cdot)$, $\chi_{6024}(2009,\cdot)$, $\chi_{6024}(4273,\cdot)$

First 32 of 2000 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{6024}(1,\cdot)$	6024.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6024}(5,\cdot)$	6024.bm	50	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{18}{25}\right)$
$\chi_{6024}(7,\cdot)$	6024.bz	250	no	$-1$	$1$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{129}{250}\right)$	$e\left(\frac{203}{250}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{77}{250}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{3}{250}\right)$
$\chi_{6024}(11,\cdot)$	6024.ch	250	yes	$-1$	$1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{203}{250}\right)$	$e\left(\frac{73}{125}\right)$	$e\left(\frac{27}{250}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{143}{250}\right)$	$e\left(\frac{32}{125}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{13}{250}\right)$	$e\left(\frac{121}{250}\right)$
$\chi_{6024}(13,\cdot)$	6024.cb	250	no	$1$	$1$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{27}{250}\right)$	$e\left(\frac{249}{250}\right)$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{41}{250}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{231}{250}\right)$	$e\left(\frac{51}{125}\right)$
$\chi_{6024}(17,\cdot)$	6024.ci	250	no	$-1$	$1$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{101}{250}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{151}{250}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{17}{250}\right)$	$e\left(\frac{7}{125}\right)$
$\chi_{6024}(19,\cdot)$	6024.cd	250	no	$1$	$1$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{143}{250}\right)$	$e\left(\frac{41}{250}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{69}{250}\right)$	$e\left(\frac{37}{250}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{77}{125}\right)$	$e\left(\frac{193}{250}\right)$
$\chi_{6024}(23,\cdot)$	6024.cl	250	no	$1$	$1$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{77}{250}\right)$	$e\left(\frac{32}{125}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{151}{250}\right)$	$e\left(\frac{37}{250}\right)$	$e\left(\frac{38}{125}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{117}{250}\right)$	$e\left(\frac{89}{250}\right)$
$\chi_{6024}(25,\cdot)$	6024.bg	25	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{11}{25}\right)$
$\chi_{6024}(29,\cdot)$	6024.ce	250	yes	$1$	$1$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{13}{250}\right)$	$e\left(\frac{231}{250}\right)$	$e\left(\frac{17}{250}\right)$	$e\left(\frac{77}{125}\right)$	$e\left(\frac{117}{250}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{139}{250}\right)$	$e\left(\frac{94}{125}\right)$
$\chi_{6024}(31,\cdot)$	6024.bz	250	no	$-1$	$1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{121}{250}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{7}{125}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{89}{250}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{94}{125}\right)$	$e\left(\frac{221}{250}\right)$
$\chi_{6024}(35,\cdot)$	6024.cg	250	yes	$1$	$1$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{119}{250}\right)$	$e\left(\frac{133}{250}\right)$	$e\left(\frac{171}{250}\right)$	$e\left(\frac{97}{250}\right)$	$e\left(\frac{57}{125}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{62}{125}\right)$	$e\left(\frac{183}{250}\right)$
$\chi_{6024}(37,\cdot)$	6024.ca	250	no	$-1$	$1$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{26}{125}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{34}{125}\right)$	$e\left(\frac{58}{125}\right)$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{1}{125}\right)$
$\chi_{6024}(41,\cdot)$	6024.ci	250	no	$-1$	$1$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{121}{125}\right)$	$e\left(\frac{219}{250}\right)$	$e\left(\frac{114}{125}\right)$	$e\left(\frac{171}{250}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{221}{250}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{207}{250}\right)$	$e\left(\frac{122}{125}\right)$
$\chi_{6024}(43,\cdot)$	6024.cd	250	no	$1$	$1$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{131}{250}\right)$	$e\left(\frac{117}{250}\right)$	$e\left(\frac{79}{250}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{11}{250}\right)$	$e\left(\frac{53}{250}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{63}{125}\right)$	$e\left(\frac{67}{250}\right)$
$\chi_{6024}(47,\cdot)$	6024.bu	50	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{7}{50}\right)$
$\chi_{6024}(49,\cdot)$	6024.bw	125	no	$1$	$1$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{4}{125}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{49}{125}\right)$	$e\left(\frac{77}{125}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{84}{125}\right)$	$e\left(\frac{3}{125}\right)$
$\chi_{6024}(53,\cdot)$	6024.ce	250	yes	$1$	$1$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{22}{125}\right)$	$e\left(\frac{233}{250}\right)$	$e\left(\frac{121}{250}\right)$	$e\left(\frac{247}{250}\right)$	$e\left(\frac{82}{125}\right)$	$e\left(\frac{97}{250}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{79}{125}\right)$
$\chi_{6024}(55,\cdot)$	6024.by	250	no	$1$	$1$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{38}{125}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{104}{125}\right)$	$e\left(\frac{59}{250}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{53}{250}\right)$	$e\left(\frac{51}{250}\right)$
$\chi_{6024}(59,\cdot)$	6024.ch	250	yes	$-1$	$1$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{23}{250}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{157}{250}\right)$	$e\left(\frac{149}{250}\right)$	$e\left(\frac{63}{250}\right)$	$e\left(\frac{112}{125}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{233}{250}\right)$	$e\left(\frac{111}{250}\right)$
$\chi_{6024}(61,\cdot)$	6024.ca	250	no	$-1$	$1$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{79}{125}\right)$	$e\left(\frac{221}{250}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{32}{125}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{37}{125}\right)$	$e\left(\frac{104}{125}\right)$
$\chi_{6024}(65,\cdot)$	6024.ci	250	no	$-1$	$1$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{63}{125}\right)$	$e\left(\frac{207}{250}\right)$	$e\left(\frac{17}{125}\right)$	$e\left(\frac{213}{250}\right)$	$e\left(\frac{53}{125}\right)$	$e\left(\frac{113}{250}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{21}{250}\right)$	$e\left(\frac{16}{125}\right)$
$\chi_{6024}(67,\cdot)$	6024.cc	250	no	$-1$	$1$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{167}{250}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{53}{250}\right)$	$e\left(\frac{98}{125}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{121}{250}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{7}{250}\right)$	$e\left(\frac{219}{250}\right)$
$\chi_{6024}(71,\cdot)$	6024.ck	250	no	$-1$	$1$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{111}{250}\right)$	$e\left(\frac{227}{250}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{143}{250}\right)$	$e\left(\frac{8}{125}\right)$	$e\left(\frac{84}{125}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{103}{125}\right)$	$e\left(\frac{177}{250}\right)$
$\chi_{6024}(73,\cdot)$	6024.bw	125	no	$1$	$1$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{91}{125}\right)$	$e\left(\frac{87}{125}\right)$	$e\left(\frac{94}{125}\right)$	$e\left(\frac{8}{125}\right)$	$e\left(\frac{21}{125}\right)$	$e\left(\frac{33}{125}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{37}{125}\right)$
$\chi_{6024}(77,\cdot)$	6024.ce	250	yes	$1$	$1$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{41}{125}\right)$	$e\left(\frac{99}{250}\right)$	$e\left(\frac{163}{250}\right)$	$e\left(\frac{91}{250}\right)$	$e\left(\frac{96}{125}\right)$	$e\left(\frac{141}{250}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{97}{250}\right)$	$e\left(\frac{62}{125}\right)$
$\chi_{6024}(79,\cdot)$	6024.bz	250	no	$-1$	$1$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{191}{250}\right)$	$e\left(\frac{37}{250}\right)$	$e\left(\frac{122}{125}\right)$	$e\left(\frac{29}{125}\right)$	$e\left(\frac{121}{250}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{237}{250}\right)$
$\chi_{6024}(83,\cdot)$	6024.cg	250	yes	$1$	$1$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{187}{250}\right)$	$e\left(\frac{209}{250}\right)$	$e\left(\frac{233}{250}\right)$	$e\left(\frac{81}{250}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{3}{125}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{26}{125}\right)$	$e\left(\frac{109}{250}\right)$
$\chi_{6024}(85,\cdot)$	6024.cb	250	no	$1$	$1$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{46}{125}\right)$	$e\left(\frac{169}{250}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{48}{125}\right)$	$e\left(\frac{127}{250}\right)$	$e\left(\frac{73}{125}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{57}{250}\right)$	$e\left(\frac{97}{125}\right)$
$\chi_{6024}(89,\cdot)$	6024.ci	250	no	$-1$	$1$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{89}{250}\right)$	$e\left(\frac{84}{125}\right)$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{56}{125}\right)$	$e\left(\frac{51}{250}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{67}{250}\right)$	$e\left(\frac{57}{125}\right)$
$\chi_{6024}(91,\cdot)$	6024.bt	50	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{21}{50}\right)$
$\chi_{6024}(95,\cdot)$	6024.ck	250	no	$-1$	$1$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{39}{250}\right)$	$e\left(\frac{73}{250}\right)$	$e\left(\frac{38}{125}\right)$	$e\left(\frac{57}{250}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{16}{125}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{123}{250}\right)$

Click here to search among the remaining 1968 characters.

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$6024$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{250}\)
Order	$2000$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{6024}(1,\cdot)\)	6024.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6024}(5,\cdot)\)	6024.bm	50	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)
\(\chi_{6024}(7,\cdot)\)	6024.bz	250	no	\(-1\)	\(1\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{129}{250}\right)\)	\(e\left(\frac{203}{250}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{77}{250}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{3}{250}\right)\)
\(\chi_{6024}(11,\cdot)\)	6024.ch	250	yes	\(-1\)	\(1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{203}{250}\right)\)	\(e\left(\frac{73}{125}\right)\)	\(e\left(\frac{27}{250}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{143}{250}\right)\)	\(e\left(\frac{32}{125}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{13}{250}\right)\)	\(e\left(\frac{121}{250}\right)\)
\(\chi_{6024}(13,\cdot)\)	6024.cb	250	no	\(1\)	\(1\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{27}{250}\right)\)	\(e\left(\frac{249}{250}\right)\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{41}{250}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{231}{250}\right)\)	\(e\left(\frac{51}{125}\right)\)
\(\chi_{6024}(17,\cdot)\)	6024.ci	250	no	\(-1\)	\(1\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{101}{250}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{151}{250}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{17}{250}\right)\)	\(e\left(\frac{7}{125}\right)\)
\(\chi_{6024}(19,\cdot)\)	6024.cd	250	no	\(1\)	\(1\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{143}{250}\right)\)	\(e\left(\frac{41}{250}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{69}{250}\right)\)	\(e\left(\frac{37}{250}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{77}{125}\right)\)	\(e\left(\frac{193}{250}\right)\)
\(\chi_{6024}(23,\cdot)\)	6024.cl	250	no	\(1\)	\(1\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{77}{250}\right)\)	\(e\left(\frac{32}{125}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{151}{250}\right)\)	\(e\left(\frac{37}{250}\right)\)	\(e\left(\frac{38}{125}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{117}{250}\right)\)	\(e\left(\frac{89}{250}\right)\)
\(\chi_{6024}(25,\cdot)\)	6024.bg	25	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)
\(\chi_{6024}(29,\cdot)\)	6024.ce	250	yes	\(1\)	\(1\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{13}{250}\right)\)	\(e\left(\frac{231}{250}\right)\)	\(e\left(\frac{17}{250}\right)\)	\(e\left(\frac{77}{125}\right)\)	\(e\left(\frac{117}{250}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{139}{250}\right)\)	\(e\left(\frac{94}{125}\right)\)
\(\chi_{6024}(31,\cdot)\)	6024.bz	250	no	\(-1\)	\(1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{121}{250}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{7}{125}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{89}{250}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{94}{125}\right)\)	\(e\left(\frac{221}{250}\right)\)
\(\chi_{6024}(35,\cdot)\)	6024.cg	250	yes	\(1\)	\(1\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{119}{250}\right)\)	\(e\left(\frac{133}{250}\right)\)	\(e\left(\frac{171}{250}\right)\)	\(e\left(\frac{97}{250}\right)\)	\(e\left(\frac{57}{125}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{62}{125}\right)\)	\(e\left(\frac{183}{250}\right)\)
\(\chi_{6024}(37,\cdot)\)	6024.ca	250	no	\(-1\)	\(1\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{26}{125}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{34}{125}\right)\)	\(e\left(\frac{58}{125}\right)\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{1}{125}\right)\)
\(\chi_{6024}(41,\cdot)\)	6024.ci	250	no	\(-1\)	\(1\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{121}{125}\right)\)	\(e\left(\frac{219}{250}\right)\)	\(e\left(\frac{114}{125}\right)\)	\(e\left(\frac{171}{250}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{221}{250}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{207}{250}\right)\)	\(e\left(\frac{122}{125}\right)\)
\(\chi_{6024}(43,\cdot)\)	6024.cd	250	no	\(1\)	\(1\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{131}{250}\right)\)	\(e\left(\frac{117}{250}\right)\)	\(e\left(\frac{79}{250}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{11}{250}\right)\)	\(e\left(\frac{53}{250}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{63}{125}\right)\)	\(e\left(\frac{67}{250}\right)\)
\(\chi_{6024}(47,\cdot)\)	6024.bu	50	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{6024}(49,\cdot)\)	6024.bw	125	no	\(1\)	\(1\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{4}{125}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{49}{125}\right)\)	\(e\left(\frac{77}{125}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{84}{125}\right)\)	\(e\left(\frac{3}{125}\right)\)
\(\chi_{6024}(53,\cdot)\)	6024.ce	250	yes	\(1\)	\(1\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{22}{125}\right)\)	\(e\left(\frac{233}{250}\right)\)	\(e\left(\frac{121}{250}\right)\)	\(e\left(\frac{247}{250}\right)\)	\(e\left(\frac{82}{125}\right)\)	\(e\left(\frac{97}{250}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{79}{125}\right)\)
\(\chi_{6024}(55,\cdot)\)	6024.by	250	no	\(1\)	\(1\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{38}{125}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{104}{125}\right)\)	\(e\left(\frac{59}{250}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{53}{250}\right)\)	\(e\left(\frac{51}{250}\right)\)
\(\chi_{6024}(59,\cdot)\)	6024.ch	250	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{23}{250}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{157}{250}\right)\)	\(e\left(\frac{149}{250}\right)\)	\(e\left(\frac{63}{250}\right)\)	\(e\left(\frac{112}{125}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{233}{250}\right)\)	\(e\left(\frac{111}{250}\right)\)
\(\chi_{6024}(61,\cdot)\)	6024.ca	250	no	\(-1\)	\(1\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{79}{125}\right)\)	\(e\left(\frac{221}{250}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{32}{125}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{37}{125}\right)\)	\(e\left(\frac{104}{125}\right)\)
\(\chi_{6024}(65,\cdot)\)	6024.ci	250	no	\(-1\)	\(1\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{63}{125}\right)\)	\(e\left(\frac{207}{250}\right)\)	\(e\left(\frac{17}{125}\right)\)	\(e\left(\frac{213}{250}\right)\)	\(e\left(\frac{53}{125}\right)\)	\(e\left(\frac{113}{250}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{21}{250}\right)\)	\(e\left(\frac{16}{125}\right)\)
\(\chi_{6024}(67,\cdot)\)	6024.cc	250	no	\(-1\)	\(1\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{167}{250}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{53}{250}\right)\)	\(e\left(\frac{98}{125}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{121}{250}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{7}{250}\right)\)	\(e\left(\frac{219}{250}\right)\)
\(\chi_{6024}(71,\cdot)\)	6024.ck	250	no	\(-1\)	\(1\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{111}{250}\right)\)	\(e\left(\frac{227}{250}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{143}{250}\right)\)	\(e\left(\frac{8}{125}\right)\)	\(e\left(\frac{84}{125}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{103}{125}\right)\)	\(e\left(\frac{177}{250}\right)\)
\(\chi_{6024}(73,\cdot)\)	6024.bw	125	no	\(1\)	\(1\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{91}{125}\right)\)	\(e\left(\frac{87}{125}\right)\)	\(e\left(\frac{94}{125}\right)\)	\(e\left(\frac{8}{125}\right)\)	\(e\left(\frac{21}{125}\right)\)	\(e\left(\frac{33}{125}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{37}{125}\right)\)
\(\chi_{6024}(77,\cdot)\)	6024.ce	250	yes	\(1\)	\(1\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{41}{125}\right)\)	\(e\left(\frac{99}{250}\right)\)	\(e\left(\frac{163}{250}\right)\)	\(e\left(\frac{91}{250}\right)\)	\(e\left(\frac{96}{125}\right)\)	\(e\left(\frac{141}{250}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{97}{250}\right)\)	\(e\left(\frac{62}{125}\right)\)
\(\chi_{6024}(79,\cdot)\)	6024.bz	250	no	\(-1\)	\(1\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{191}{250}\right)\)	\(e\left(\frac{37}{250}\right)\)	\(e\left(\frac{122}{125}\right)\)	\(e\left(\frac{29}{125}\right)\)	\(e\left(\frac{121}{250}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{237}{250}\right)\)
\(\chi_{6024}(83,\cdot)\)	6024.cg	250	yes	\(1\)	\(1\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{187}{250}\right)\)	\(e\left(\frac{209}{250}\right)\)	\(e\left(\frac{233}{250}\right)\)	\(e\left(\frac{81}{250}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{3}{125}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{26}{125}\right)\)	\(e\left(\frac{109}{250}\right)\)
\(\chi_{6024}(85,\cdot)\)	6024.cb	250	no	\(1\)	\(1\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{46}{125}\right)\)	\(e\left(\frac{169}{250}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{48}{125}\right)\)	\(e\left(\frac{127}{250}\right)\)	\(e\left(\frac{73}{125}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{57}{250}\right)\)	\(e\left(\frac{97}{125}\right)\)
\(\chi_{6024}(89,\cdot)\)	6024.ci	250	no	\(-1\)	\(1\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{89}{250}\right)\)	\(e\left(\frac{84}{125}\right)\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{56}{125}\right)\)	\(e\left(\frac{51}{250}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{67}{250}\right)\)	\(e\left(\frac{57}{125}\right)\)
\(\chi_{6024}(91,\cdot)\)	6024.bt	50	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{21}{50}\right)\)
\(\chi_{6024}(95,\cdot)\)	6024.ck	250	no	\(-1\)	\(1\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{39}{250}\right)\)	\(e\left(\frac{73}{250}\right)\)	\(e\left(\frac{38}{125}\right)\)	\(e\left(\frac{57}{250}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{16}{125}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{123}{250}\right)\)

Introduction

L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.